Water flows steadily from an open tank as shown in the figure. (Figure 1) The el

Question

Water flows steadily from an open tank as shown in the figure. (Figure 1) The elevation of point 1 is10.0 m , and the elevation of points 2 and 3 is2.00 m . The cross-sectional area at point 2 is4.80×102 m2 ; at point 3, where the water is discharged, it is 1.60×102 m2 . The cross-sectional area of the tank is very large compared with the cross-sectional area of the pipe.

Assuming that Bernoulli's equation applies, compute the volume of water V that flows across the exit of the pipe in 1.00 s . In other words, find the discharge rate V/t.

Express your answer numerically in cubic meters per second.

Explanation / Answer

use bernoulli's equation for 1 to 3, take v1 to equal zero and P3 = P1

P1/pg + z1 = P3/pg + v3^2/2g + z3

v3 = sqrt(2g(z1 - z3)) = sqrt(2*9.81(10 - 2)) = 12.53 m/s

Q = A3*v3 = .2005 m^3/s

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